On the existence of a limit value in some non expansive optimal control problems, and application to averaging of singularly perturbed systems

Marc Quincampoix (1) , Jérôme Renault (2, 3)

1 LM-Brest - Laboratoire de Mathématiques
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 CECO - Laboratoire d'économétrie de l'École polytechnique

We investigate a limit value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it is usually done in the literature. We apply this new result to study a singularly control perturbed system, and we obtain a description of the limit dynamics in term of a differential inclusion.

Domaines: Optimisation et contrôle [math.OC]

Marc Quincampoix, Jérôme Renault. On the existence of a limit value in some non expansive optimal control problems, and application to averaging of singularly perturbed systems. 2009. ⟨hal-00377857v1⟩